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In this paper, we show that the stabilizer subgroup of Df = {a ∈ Fq | f (a) ∈ (F×q )2} for a f ∈ Fq [x] without multiple roots can be derived from the stabilizer of Df = {a ∈ Fq | f (a) = 0} ∪ {∞}. As an application, we construct a family of 3-designs such as 3 − ( q + 1, q−1 2 , (q−1)(q−3)(q−5) 16 ) , where q is a prime power such that q ≡ 3 (mod 4) and q(More)
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